Is there a Möbius band in closed protein beta-sheets?

Area of Science:

• Structural bioinformatics
• Protein structure analysis
• Computational biology

Background:

• Protein beta-sheets are fundamental to protein structure and folding.
• Understanding the topology of beta-sheets, including closed structures, is key to deciphering protein function.
• Previous studies have not fully characterized the topological properties of complex beta-sheet arrangements.

Purpose of the Study:

• To define and characterize bifurcations and pseudobifurcations in protein beta-sheets.
• To introduce a method for determining the one- or two-sidedness of closed beta-sheet surfaces.
• To investigate the occurrence of specific beta-sheet topologies within the Protein Data Bank.

Main Methods:

• Development of definitions for bifurcations and pseudobifurcations in beta-sheets.
• Introduction of a characteristic number to assess surface topology (one- vs. two-sided).
• Systematic search of the Protein Data Bank (April 1997 release) using DSSP definitions for beta-structures.

Main Results:

• No one-sided beta-Möbius bands were found in the analyzed Protein Data Bank.
• Identified beta-structures with an odd number of antiparallel ladders and bifurcations.
• Discovered beta-structures closed at a singular point, which can be modified into one- or two-sided surfaces by adding patches.
• The catalytic triad of GMP synthetase (1GPM) is located near such a singular point.

Conclusions:

• The study provides a topological framework for analyzing complex protein beta-sheet structures.
• The absence of one-sided beta-Möbius bands suggests specific constraints in protein folding or evolutionary selection.
• The identified singular point structures offer insights into protein engineering and functional site localization, as exemplified by GMP synthetase.